Qiuyun TMUA Simulation Test Paper 1 · Question 20

If $x$ is a real number, let $\lfloor x\rfloor$ be the greatest integer that is less than or equal to $x$ . If $n$ is a positive integer, let $S(n)$ be defined by

S(n)=\left\lfloor\frac n{10^{\lfloor\log n\rfloor}}\right\rfloor+10\left(n-10^{\lfloor\log n\rfloor}\times\left\lfloor\frac n{10^{\lfloor\log n\rfloor}}\right\rfloor\right).

(All the logarithms are base 10.)

How many integers $n$ from 1 to 2011 (inclusive) satisfy $S(S(n))=n$ ?

108

104

100

96

92

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Qiuyun TMUA Simulation Test Paper 1 · Q20